Solve in positive integers the cubic
The solution (obviously) is 13 but you know how Dirty n Untidy n Ugly the cubic equations are to solve!!
If anyone's got a Good way to solve the above, please let me know!!:cool:
If two or more thoughts intersect, there has to be a point!
"Data! Data! Data!" he cried impatiently. "I can't make bricks without clay."
He probably graphed the equation and eyeballed the root as 13. This is an acceptable conjecture which can be proved by plugging in. A little fortuitious but... Then it is trival to prove that it is the only positive root.
You would deflate out the obvious root.
The discriminant of the right side is - 472, so 13 is the only positive root.
If it ain't broke, fix it until it is.
No great discovery was ever made without a bold guess.
Another way is to use the method developed for solving a general cubic. It is given in a thread of mine and is available on the net.
Taking a new step, uttering a new word, is what people fear most. ― Fyodor Dostoyevsky, Crime and Punishment
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